Q105 / 180 · COMEDK 2013 · Mathematics

If $\frac{\log x}{a-b}=\frac{\log y}{b-c}=\frac{\log z}{c-a}$, then $x y z$ is equal to

  • A
    $0$
  • Correct answer
    B
    $1$
  • C
    $-1$
  • D
    $2$

Solution

Let $\frac{\log x}{a-b}=\frac{\log y}{b-c}=\frac{\log z}{c-a}=k$ $\Rightarrow \quad \log x=k(a-b)$, $\log y=k(b-c)$ and $\quad \log z=k(c-a)$ Now' $\log x+\log y+\log z=$ $k(a-b+b-c+c-a)$ $\Rightarrow \quad \log (x y z)=0$ $\Rightarrow \quad x y z=1$

Hence, the correct answer is option: 'B'.

Relevant Questions